Math Lessons for a Living Education: Level 5

First printing: March 2016 Sixth printing: March 2021

Copyright © 2016 by Angela O’Dell, Kyrsten Carlson, and Master Books®. All rights reserved. No part of this book may be reproduced, copied, broadcast, stored, or shared in any form whatsoever without written permission from the publisher, except in the case of brief quotations in articles and reviews. For information write:

Master Books®, P.O. Box 726, Green Forest, AR 72638Master Books® is a division of the New Leaf Publishing Group, Inc.

ISBN: 978-0-89051-927-1ISBN: 978-1-61458-515-2 (digital)

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Unless otherwise noted, Scripture quotations are from the New King James Version of the Bible.

Printed in the United States of America

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DedicationTo my favorite students, who were also my teachers.

I love you!.

Author Bio:As a homeschooling mom and author, Angela O’Dell embraces many aspects of the Charlotte Mason method yet knows that modern children need an education that fits the needs of this generation. Based upon her foundational belief in a living God for a living education, she has worked to bring a curriculum that will reach deep into the heart of home-educated children and their families. She has written over 20 books, including her history series and her math series. Angela’s goal is to bring materials that teach and train hearts and minds to find the answers for our generation in the never-changing truth of God and His Word.

Faith Grower

Author: Angela O’Dell Kyrsten Carlson

Master Books Creative Team:

Editor: Craig Froman

Design: Terry White

Cover Design: Diana Bogardus

Copy Editors: Judy Lewis Willow Meek

Curriculum Review: Kristen Pratt Laura Welch Diana Bogardus

Permission is granted for copies of reproducible pages from this text to be made for use with immediate family members living in the same household. However, no part of this book may be reproduced, copied, broadcast, stored, or shared in any form beyond this use. Permission for any other use of the material must be requested by email from the publisher at [email protected].

Scope and Sequence Using this Course ..................................................................................................................................................4Schedule .................................................................................................................................................................8Lesson 1: Review of All Addition and Subtraction Concepts ...................................................................... 15Lesson 2: Review of All Division and Multiplication .................................................................................... 21Lesson 3: Review of All Geometry .................................................................................................................. 27Lesson 4: Review of All Measurement ............................................................................................................ 35Lesson 5: Review of All Fractions Concepts .................................................................................................. 41Lesson 6: Review of All Decimal Concepts .................................................................................................... 47Lesson 7: 10, 100, 1,000 (multiplying/dividing) ............................................................................................ 53Lesson 8: Introduction to 2-Digit Divisors .................................................................................................... 63Lesson 9: More Work with Division ................................................................................................................ 73Lesson 10: Three Ways of Division/Remainders as Fractions ...................................................................... 81 Lesson 11: Review Week ................................................................................................................................... 91Lesson 12: Factoring .......................................................................................................................................... 99Lesson 13: Common Factors, Greatest Common Factor, and Reducing Fractions ............................... 107Lesson 14: Proper and Improper Fractions ................................................................................................. 115Lesson 15: Working with Improper Fractions ............................................................................................ 123Lesson 16: Sums Containing improper Fractions ...................................................................................... 129Lesson 17: Least Common Multiples ........................................................................................................... 137Lesson 18: Least Common Multiples/Finding a Common Denominator .............................................. 145Lesson 19: Review of All New Concepts ...................................................................................................... 155Lesson 20: Adding Fractions with Uncommon Denominators ................................................................ 161 Lesson 21: Subtracting Fractions with Uncommon Denominators ......................................................... 169Lesson 22: Subtracting Mixed Numbers with Carrying & Borrowing - Common Denominators ..... 177Lesson 23: Adding Mixed Numbers with Carrying — Uncommon Denominators .............................. 185Lesson 24: Subtracting Mixed Numbers with Borrowing — Uncommon Denominators.................... 193Lesson 25: Review! .......................................................................................................................................... 201Lesson 26: Multiplying Fractions .................................................................................................................. 207Lesson 27: Divisibility Rules & Dividing Fractions .................................................................................... 217Lesson 28: Multiplying Decimals .................................................................................................................. 223Lesson 29: Dividing Decimals ....................................................................................................................... 229Lesson 30: Hands On! Counting Back Money ............................................................................................ 235Lesson 31: Review of All Division ................................................................................................................ 239Lesson 32: Review of Factoring, Common Factors, & Greatest Common Factors ................................ 243Lesson 33: Review of Fractional Concepts Part 1 ...................................................................................... 249 Lesson 34: Review of Fractional Concepts Part 2 ....................................................................................... 255Lesson 35: Review of Multiplying and Dividing Fractions ....................................................................... 261Lesson 36: Review of Multiplying and Diving Decimals ........................................................................... 267Manipulatives .................................................................................................................................................. 273Solutions Manual ............................................................................................................................................ 285

Using This Course

Features: The suggested weekly schedule enclosed has easy-to-manage lessons that guide the reading, worksheets, and all assessments. The pages of this course are perforated and three-hole punched so materials are easy to tear out, hand out, grade, and store. Teachers are encouraged to adjust the schedule and materials needed in order to best work within their unique educational program.

Lesson Scheduling: Students are instructed to read the pages in their book and then complete the corresponding section provided by the teacher. Assessments that may include worksheets, activities, quizzes, and tests are given at regular intervals with space to record each grade. Space is provided on the weekly schedule for assignment dates, and flexibility in scheduling is encouraged. Teachers may adapt the scheduled days per each unique student situation. As the student completes each assignment, this can be marked with an “X” in the box.

Course DescriptionWelcome to the fifth book in the Math Lessons for a Living Education series! You will find that Math Lessons for a Living Education is a unique approach to learning math. A blend of stories, copy work, oral narration, and hands-on experience brings the concepts to life and invites the child to explore the world around them. The tone of this math book is meant to speak personally to each child, and the method easily adapted to any teaching style.

The first 30 lessons have a story about the twins, taught through hands-on learning. After the story, there are exercises for students to practice the lesson they learned and to review what they have learned earlier. The first lessons provide review time, and the last 6 lessons are focused reviews, covering topics learned throughout the first 30 lessons.

Approximately 30 minutes per lesson, five days a week, for 36 weeksSolution Manual for worksheets is available in the back of this book

Review sections can be used as quizzes

Worksheets are included for each section

Designed for grade 5 in a one-year course

4 Math Level 5

Course Objectives: Students completing this course will

DReview basic operations DExplore new concepts like fractions, mixed numbers, decimals, and percents DLearn how to find greatest common factor and least common multiple DAdd, subtract, multiply, and divide decimals.

Teaching mathematics as a living subject

As a teacher and a mother, I have discovered that true education is based on relationships: the relationship the child makes with the amazing concepts in the world around them; the relationship the teacher and the child make with each other; and most importantly and ultimately, the relationship the child makes with their Creator. It is built on discovering the God of the Universe — the One who holds the universe in His hands, but at the same time, lovingly dwells in the heart of a little child. The story in Book 5 is meant to reach into a child’s world, grab their attention and invite them into the learning process. The concepts are not taught through drill only, but also through

encouraging the student to hone their critical thinking skills and think outside of the box. This curriculum teaches the student math, but it is not result-oriented, focusing only on grades; instead it is skill and process-oriented. I have discovered that it is in the everyday that we grow and become who we are meant to be. It is in the little discoveries all along the path of life that we grow, learn, develop, and discover who God is and, in turn, see ourselves the way He sees us. Math concepts are learned well, as it is learned in the context of living, in the midst of discovery, and through the worldview glasses that focus on the bigger picture.

5Math Level 5

About manipulatives In the back of the book, you will find a manipulatives section. It is imperative that you prepare these before you start the book. You will need these resources: 1. contact paper and construction paper2. large index cards3. brass fasteners4. crayons, markers, and colored pencils5. glue or paste6. hole punch and hole reinforcers7. rings to keep flashcards together8. a plastic shoe box with lid in which to store

manipulatives9. (optional but helpful) stickers to use for

flashcards

10. pictures from old magazines11. poster board (several large pieces)12. foot ruler (with inches marked)13. simple indoor/outdoor thermometer

(non-digital)14. rice15. measuring devices

• cup set: 1 cup, 12 cup, 1

4 cup, 13 cup

• spoon set: 1 tbs, 12 tbs, 1 tsp, 1

2 tsp, 14 tsp

• large plastic bowls (mixing bowls or ice cream buckets)

Grading subjective assignmentsMost often with math the grading is very objective. For example, 2 + 2 = 4, and no amount of individual expression changes this answer. However, there are times in this course when the answer may depend on a student’s reflections of what he or she has learned on a particular day or in a week of assignments. In these subjective cases, the teacher can base a grade for these responses on several more objective measures. Does the student seem to understand the question and answer it as clearly as possible? Does the answer seem complete or does it fail to answer all aspects of the question? So a student may receive full credit if they seemed to meet all the assignment requirements, may get a passing grade if they meet some of the requirements, or may need to repeat the assignment if they didn’t meet any of the requirements.

A – Student showed complete mastery of concepts with no errors.

B – Student showed mastery of concepts with minimal errors.

C – Student showed partial mastery of concepts. Review of some concepts is needed.

D – Student showed minimal understanding of concepts. Review is needed.

F – Student did not show understanding of concepts. Review is needed.

6 Math Level 5

How to use everyday items as manipulatives

Note to the teacher:

Welcome to Math Lessons for a Living Education Book 5. If this is your first year using this math curriculum, please take the time before you start, in order to familiarize yourself with the layout of the course. Math Lessons for a Living Education uses a unique approach to teaching and learning math concepts. Unlike many math curriculums, Math Lessons For a Living Education does not focus on memorization of computation to the exclusion of conceptual and critical understanding. In this course, you will find plenty of practice and reinforcement of concepts and computation. This is not a course that will allow students to quickly shove facts into their short term memories for the sole purpose of passing a quiz and getting a good grade. Grades are not the focus of this course; long term understanding and developed critical thinking skills are the desired outcome and will form a firm foundation on which higher math can be built.

Before you begin this book, please make sure you have prepared the charts from the manipulatives section. You may laminate a copy of each chart for each student, or if you prefer, make copies to store in a file and distributed as needed throughout the year.

Here is a list of topics that are used as crosscurricular focuses throughout the year. You may wish to have library books about topics of interest.

• the country of Peru• a good Bible story book• recipe books (or boxes)• the history of the Volkswagen “Bug”• Dewey Decimal System• recycling• Mexico• Creation Science vs. Evolution• Ancient Mayans• auto mechanics shop• the art of quilting• Christmas traditions• banks and personal financing• geometry-focused books• wilderness survival

7Math Level 5

First Semester Suggested Daily Schedule

Date Day Assignment Due Date GradeFirst Semester-First Quarter

Week 1

Day 1 Read Lesson 1 • Page 15 Complete Lesson 1 Exercise 1 Review Week • Page 16

Day 2 Complete Lesson 1 Exercise 2 • Page 17Day 3 Complete Lesson 1 Exercise 3 • Page 18Day 4 Complete Lesson 1 Exercise 4 • Page 19Day 5 Complete Lesson 1 Exercise 5 • Page 20

Week 2

Day 6 Read Lesson 2 • Page 21Complete Lesson 2 Exercise 1 Review Week • Page 22


Week 3

Day 11 Read Lesson 3 • Pages 27-28Complete Lesson 3 Exercise 1 Review Week • Pages 29-30


Week 4



Week 5

Day 21 Read Lesson 5 • Pages 41-42Complete Lesson 5 Exercise 1 Review Week • Page 43

Day 22 Complete Lesson 5 Exercise 2 • Page 44Day 23 Complete Lesson 5 Exercise 3 • Page 45Day 24 Begin Lesson 5 Exercise 4-5 • Page 46Day 25 Finish Lesson 5 Exercise 4-5 • Page 46

Week 6



8 Math Level 5

Date Day Assignment Due Date Grade

Week 7

Day 31 Read Lesson 7 • Pages 53-54 Complete Lesson 7 Exercise 1 • Page 55

Day 32 Complete Lesson 7 Exercise 2 • Pages 56-57Day 33 Complete Lesson 7 Exercise 3 • Pages 58-59Day 34 Complete Lesson 7 Exercise 4 • Page 60Day 35 Complete Lesson 7 Exercise 5 • Pages 61-62

Week 8

Day 36 Read Lesson 8 • Pages 63-64Complete Lesson 8 Exercise 1 • Pages 65-66

Day 37 Complete Lesson 8 Exercise 2 • Pages 67-68Day 38 Complete Lesson 8 Exercise 3 • Pages 69-70Day 39 Begin Lesson 8 Exercise 4 • Pages 71Day 40 Finish Lesson 8 Exercise 5 • Pages 72

Week 9

Day 41 Read Lesson 9 • Pages 73-74 Complete Lesson 9 Exercise 1 • Pages 75-76

Day 42 Complete Lesson 9 Exercise 2 • Page 77Day 43 Complete Lesson 9 Exercise 3 • Pages 78-79Day 44 Begin Lesson 9 Exercise 4-5 Review Time • Page 80Day 45 Finish Lesson 9 Exercise 4-5 Review Time • Page 80

First Semester-Second Quarter

Week 1


Day 47 Complete Lesson 10 Exercise 2 • Page 85Day 48 Complete Lesson 10 Exercise 3 • Pages 86-87Day 49 Complete Lesson 10 Exercise 4 • Pages 88-89Day 50 Complete Lesson 10 Exercise 5 • Page 90

Week 2

Day 51 Read Lesson 11 • Page 91 Complete Lesson 11 Exercise 1 Review Week • Pages 92-93

Day 52 Complete Lesson 11 Exercise 2 • Page 94 Day 53 Complete Lesson 11 Exercise 3 • Page 95Day 54 Complete Lesson 11 Exercise 4 • Pages 96-97Day 55 Complete Lesson 11 Exercise 5 • Page 98

Week 3


Day 57 Complete Lesson 12 Exercise 2 • Page 103Day 58 Complete Lesson 12 Exercise 3 • Page 104Day 59 Complete Lesson 12 Exercise 4 • Page 105Day 60 Complete Lesson 12 Exercise 5 Review Time • Page 106

Week 4

Day 61 Read Lesson 13 • Page 107Complete Lesson 13 Exercise 1 • Pages 108-109

Day 62 Complete Lesson 13 Exercise 2 • Page 110Day 63 Complete Lesson 13 Exercise 3 • Page 111Day 64 Complete Lesson 13 Exercise 4 • Page 112Day 65 Complete Lesson 13 Exercise 5 Review Time • Pages 113-114

9Math Level 5


Week 5



Week 6

Day 71 Read Lesson 15 • Page 123Complete Lesson 15 Exercise 1 • Page 124


Week 7

Day 76 Read Lesson 16 • Pages 129-130Complete Lesson 16 Exercise 1 • Page 131

Day 77 Complete Lesson 16 Exercise 2 • Page 132Day 78 Complete Lesson 16 Exercise 3 • Pages 133-134Day 79 Complete Lesson 16 Exercise 4 • Page 135Day 80 Complete Lesson 16 Exercise 5 Review Time • Page 136

Week 8


Day 82 Complete Lesson 17 Exercise 2 • Pages 140-141Day 83 Complete Lesson 17 Exercise 3 • Page 142Day 84 Complete Lesson 17 Exercise 4 • Page 143Day 85 Complete Lesson 17 Exercise 5 Review Time • Page 144

Week 9


Day 87 Complete Lesson 18 Exercise 2 • Pages 149-150Day 88 Complete Lesson 18 Exercise 3 • Page 151Day 89 Complete Lesson 18 Exercise 4 • Pages 152Day 90 Complete Lesson 18 Exercise 5 Review Time • Pages 153-154

Mid-Term Grade

10 Math Level 5

Second Semester Suggested Daily Schedule

Date Day Assignment Due Date GradeSecond Semester-Third Quarter

Week 1

Day 91 Read Lesson 19 • Page 155 Complete Lesson 19 Exercise 1 • Page 156


Week 2


Day 97 Complete Lesson 20 Exercise 2 • Page 164Day 98 Complete Lesson 20 Exercise 3 • Pages 165-166Day 99 Complete Lesson 20 Exercise 4 • Page 167Day 100 Complete Lesson 20 Exercise 5 Review Time • Page 168

Week 3

Day 101 Read Lesson 21 • Pages 169-170 Complete Lesson 21 Exercise 1 • Page 171

Day 102 Complete Lesson 21 Exercise 2 • Page 172Day 103 Complete Lesson 21 Exercise 3 • Page 173Day 104 Complete Lesson 21 Exercise 4 • Page 174 Day 105 Complete Lesson 21 Exercise 5 • Pages 175-176

Week 4


Day 107 Complete Lesson 22 Exercise 2 • Page 180Day 108 Complete Lesson 22 Exercise 3 • Page 181Day 109 Complete Lesson 22 Exercise 4 • Pages 182-183Day 110 Complete Lesson 22 Exercise 5 Review Time • Page 184

Week 5


Day 112 Complete Lesson 23 Exercise 2 • Page 189Day 113 Complete Lesson 23 Exercise 3 • Page 190Day 114 Begin Lesson 23 Exercise 4-5 • Pages 191-192Day 115 Finish Lesson 23 Exercise 4-5 • Pages 191-192

Week 6



11Math Level 5


Week 7



Week 8


Day 127 Complete Lesson 26 Exercise 2 • Page 211Day 128 Complete Lesson 26 Exercise 3 • Pages 212-213Day 129 Complete Lesson 26 Exercise 4 • Page 214Day 130 Complete Lesson 26 Exercise 5 • Pages 215-216

Week 9

Day 131 Read Lesson 27 • Page 217 Begin Lesson 27 Exercise 1 • Page 218

Day 132 Finish Lesson 27 Exercise 2 • Page 219Day 133 Begin Lesson 27 Exercise 3 • Page 220Day 134 Finish Lesson 27 Exercise 4 • Page 221Day 135 Complete Lesson 27 Exercise 5 • Page 222

Second Semester-Fourth Quarter

Week 1



Week 2



Week 3

Day 146 Read Lesson 30 • Page 235 Complete Lesson 30 Exercise 1 • Page 236

Day 147 Complete Lesson 30 Exercise 2 • Page 237Day 148 Complete Lesson 30 Exercise 3 • Page 238Day 149 Complete Lesson 30 Exercise 4 • Page 239Day 150 Complete Lesson 30 Exercise 5 Review Time • Page 240

12 Math Level 5


Week 4



Week 5



Week 6


Day 162 Complete Lesson 33 Exercise 2 • Page 255Day 163 Complete Lesson 33 Exercise 3 • Page 256Day 164 Complete Lesson 33 Exercise 4 • Page 257

Day 165 Complete Lesson 33 Exercise 5 • Page 258

Week 7


Day 167 Complete Lesson 34 Exercise 2 • Page 261Day 168 Complete Lesson 34 Exercise 3 • Page 262Day 169 Complete Lesson 34 Exercise 4 • Page 263

Day 170 Complete Lesson 34 Exercise 5 • Page 264

Week 8



Week 9



Final Grade

13Math Level 5

15Math Level 5 – Lesson 1

LessonReview of All Addition and Subtraction

1There was much excitement in the Stevens household. The four older children had volunteered to help with the younger classes at their church’s fall VBS. Their church had been serving the community and surrounding areas with this outreach for twenty-five years, and this year’s VBS was going to be a celebration! There was a record number of children signed up, and there was a lot to do to get ready. Each of the Stevens children were in charge of a craft, song, and game with the younger children.

Charlie was signed up to work with the six and seven year old boys. They were going to learn and put on a skit depicting some of the miracles of Jesus. Hairo was going to work with the same boys learning some songs and building props for the skits. Charlotte was going to help take care of the kindergarten age children, and Natty was going to help lead the worship songs with all of the age groups. Natty was also going to do something special. Mrs. Andrews, the VBS organizer, had asked Natty to share her story with all of the children during one of the morning sessions. Natty had agreed, but now she was so nervous! She had been working on what she was going to say to the group.

“Mom! I have gone through at least ten pieces of paper! I can’t seem to get my thoughts down,” Natty sighed in frustration.

“Do you want me to help, Natty?” Charlotte asked her sister.“I don’t know. In fact, I don’t know WHY I said I would do this!” Natty scowled as she balled up yet

another piece of paper and threw it, rather forcefully, into the wastebasket. “I just can’t seem to be able to sort through my thoughts. They are all jumbled,” Natty sighed again as she took a clean piece of paper and started over.

“I know! Maybe you could use math to tell your story!” Charlie suggested. Charlie thought the answer to all of life’s problems was MATH. Out of all of the Stevens children, Charlie loved math the most. In fact, math was probably his most favorite thing in the world. Math and cars.

“Oh Charlie!” Natty started to giggle. “How could math help me? My story has nothing to do with math!”

“Well, I don’t know about that! All of us here could say that Jesus SUBTRACTED our sins away from us when He died for us on the cross, and then He ADDED us to His family. And because we love and obey Him, He MULTIPLIES our blessings! And of course, He said that when He comes again, He will DIVIDE the wheat — that’s us — from the chaff — that’s the ones who don’t choose to follow Him! If that isn’t math, I don’t know what is!” Charlie finished with a flourish.

“Oh Charlie,” Natty gasped between giggles, “you need to be a preacher! And you are right! Your math did help me! I know what I am going to write now!”

16 Math Level 5 – Lesson 1

Name Exercise 1 Day 1

Mental Math

20 + 8 + 6 + 1 1 + 3 + 5 = 1 10 + 120 + 350 =

1,090 + 10 + 100 = 650 + 40 + 8 + 2 =

200 + 60 + 9 + 10 = 4,001 + 9 + 80 =

Facts review. Work quickly.

+ 4 6 10 8 2 3 5 1 9 7 0

6

+ 6 4 8 0 1 2 9 3 5 7 10

9

+ 2 5 8 1 10 3 6 4 0 7 9

8

+ 8 2 9 6 0 7 1 4 3 10 5

7



Addition review.

520

294+ 24

6 13

356+ 7 13

95,01 1+ 15,219

90,345+ 43,82 1

38

25

35+ 14

24

3 1

26+ 1 5

4 1

86

26+ 38

Fill in the blanks. Write the subtraction equation you used to solve the problem underneath it. The first one is done for you.

8 + 7 = 15 5 + ______ = 1 1 4 + ______ = 14

15 – 8 = 7

9 + ______ = 17 7 + ______ = 12 9 + ______ = 12

10 + ______ = 20 8 + ______ = 16 8 + ______ = 17

3 + ______ = 1 1 2 + ______ = 12 7 + ______ = 16



Subtraction review.

9,000_ 6,826

3,055_ 2,245

20,020_ 1 2, 1 72

52,03 1_ 10,729

Need more practice?

300– 144

600– 149

300– 226

Fill in the blanks. Write the addition equation you used to solve the problem underneath it. The first one is done for you.

17 – 8 = 9 12 – ______ = 6 16 – ______ = 7

8 + 9 = 17

16 – ______ = 8 20 – ______ = 10 15 – ______ = 9

14 – ______ = 9 13 – ______ = 8 5 – ______ = 5

21 – ______ = 1 1 19 – ______ = 1 1 18 – ______ = 15



Word Problems:1. When Grandpa Stevens took the children to the State Fair, they counted 24 big rides in one area of the

midway, 19 smaller rides in the children’s area, and 15 rides along the old-fashioned board walks in the “Ole’ Western Days” area. How many rides did they count all together at the fair?

2. How many more rides did they count in the midway than the children’s area?

3. At the fair, Charlie bought cotton candy for $1.75, Hairo bought an ice-cream cone for $2.25, and Charlotte and Natty combined their money to buy a funnel cake for $5.90. How much money did they all spend together?

4. How much more did the girls pay for the funnel cake than Charlie paid for his cotton candy?

5. What addition clue words do you look for in a word problem?

6. What subtraction clue words do you look for in a word problem?



Teac

her

Please take the time to make sure your student(s) completely understand the process of solving word problems as seen on the previous page. Use this exercise to talk through this process.

Write your own word problems and solve them. Narrate to your teacher the steps of solving an addition word problem and a subtraction word problem.

My addition word problems...1.

2.

My subtraction word problems...1.

2.


LessonFactoring 12“Mom, do you think there is something that Natty and I could do like Charlie and Hairo?” Charlotte asked with her arms in the soapy dishwater. She had soap suds up to her elbows as she stood on the stool, scrubbing cookie sheets. She and Natty had made oatmeal raisin cookies for snack.

“I don’t know Charlotte. Would you and Natty like to volunteer at the library? I heard Mrs. Drew saying that they are short on volunteers this fall. You wouldn’t get paid for it, but it would be a nice opportunity for you!” Maddie Stevens answered thoughtfully.

“Oh yes! I know I would love to do that! I’ll ask Natty, and if she wants to help, may we go today after school? Please?” Charlotte asked excitedly as she wiped her hands on the towel.

“Yes, that would be fine. Just make sure you both have finished your independent work first, okay?” her mom answered with a smile...

“We are going to head on down to the library now, Mom!” Charlotte called from the hallway. She and Natty had excitedly finished their school work, had their afternoon snack, and carefully brushed their hair. (Both of the girls were sporting a new hair-do, and they loved their new bangs!)

“Ok, make sure you are home by 5:30 though!” their mother called back from the kitchen. “And both of you make sure you take a jacket!”

“We have them, Mom,” they answered together. Linking arms, the girls skipped down the sidewalk and turned left down the street. Their house was only two blocks from the library, which meant they could go there by themselves.

“Mrs. Drew, we are here to sign up as library volunteers!” Natty said, smiling up at the tall lady behind the library desk. “Our mom says that we can volunteer after school, three days a week - just not Wednesdays because of Bible club that evening. Can you use our help?”

“Oh my, YES! You girls are an answer to my prayer! I’ve lost my helper, because Mrs. Snowden is finished working here with me - she’s about to have her first baby, you know,” Mrs. Drew whispered to the girls. Mrs. Drew always whispered - she had a lot of practice talking in her “library voice.”

The girls nodded. They knew Mrs. Snowden was about to have her baby; Mom had just mentioned that this morning during prayer time.

“Mrs. Drew, can you show us how we can help?” Charlotte asked. Mrs. Drew tended to be a little absent minded, and sometimes had to be reminded what she was doing.


“Oh. Oh, yes, of course. Silly me,” Mrs. Drew brought her attention back to the girls. “I was just thinking about my first baby...” The lady stood to her feet and came around the desk to the girls. “First,” she instructed, “you two need to know about the Dewey Decimal System. Do either of you know anything about that? No? Well, ok, that is the best place to start...”

“Mrs. Drew told us about the Dewey Decimal System today, Mom!” Charlotte told

her mom as she wiped off the kitchen table after supper. “She told us that it is like a big family tree, because it has branches like a tree.” Charlotte giggled. Mrs. Drew was a very descriptive person and used rather flowery words. “Anyway, we learned about how each type of book in the library has its own numbers to tell us what branch it belongs to. It’s still kinda confusing to me, but I know I’ll get better as I practice. How ‘bout you, Natty? Do you understand the Dewey Decimal System?” Charlotte asked her sister.

“Not really. But I’ll get it,” Natty answered. “Mom, what is the Dewey Decimal system for?” she asked her mother.

“Oh, I’m sure Mrs. Drew will tell you all about it!” their mom smiled. “But to put it simply, it’s for organizing all of the books. In a way, it’s similar to the charts you two do in math. In fact, in some ways, it’s similar to factoring, which is our next new concept in math. Do you think you girls are going to enjoy working at the library?” she asked them in a whisper.

“Yes!” they both whispered back.

Just for fun!These are called “factor trees”! (This is one way to find factors. You will learn the other way in Exercise 1.)

15

3 5

16

2

2

2

4

2

8

18

2

3 3

9

24

2

2

2

6

3

12



New Concept!Factors are all of the different numbers that divide evenly (without a remainder) into a number. Pairs of factors are two numbers that, when multiplied together, equal this number. Are you confused? Study these examples.Example #1: Find the factors of 15.

Pairs of Factors Factors1 x 15 3 x 55 x 315 x 1

1, 3, 5, 15

Example #2: Find the factors of 9.

Pairs of Factors Factors1 x 9 3 x 39 x 1

1, 3, 9

Now you try it!Find the pairs of factors of each of these numbers and list them in order from least to greatest.

Pairs of Factors for 8 Factors_____________

_____________

_____________

_____________

_____, _____, _____, _____


_____________

_____________

_____________

_____, _____, _____, _____

When we list the factors, we write each one only once, from least to greatest.


Pairs of Factors for 7 Factors

_____________

__________________, _____,


_____________

_____________

_____________

_____________

_____________

_____, _____, _____, _____, _____, _____

Review!On Monday, Charlotte and Natty worked at their lemonade stand from 2:30 to 3:45 p.m. Then they worked at the library from 4:00 to 5:30 p.m. How long did they work on Monday?



Practice the new concept!Complete the pairs of factors for these numbers.

18 20 351 x _____

2 x _____ 3 x _____ 6 x _____ 9 x _____ 18 x _____

1 x _____

2 x _____ 4 x _____ 5 x _____ 10 x _____ 20 x _____

1 x _____

5 x _____ 7 x _____ 35 x _____

Now list the factors for each of the numbers above.

18 _________________________

20 _________________________

35 _________________________

Mixed Review!

Divide and write the remainders as fractions.

2 1 8 4 0 1 5 3 1 3

Solve these mixed number problems.

203 1719

– 1 87 919

8738

+ 1928




Copywork of new concept!

Factors are all of the different numbers that divide evenly (without a remainder) into a number. Pairs of factors are two numbers that, when multiplied together, equal this number.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

More practice of the new concept!Write the pairs of factors. Note: These numbers are called prime numbers. Their only factors are 1 and themselves.

5 3 7 1 1

_____________

_____________

_____________

_____________

_____________

_____________

_____________

_____________

Write any three factors for each of these numbers. Optional: write all of the factors for each of the following numbers.

24 _______________________ 27 _______________________

32 _______________________ 64 _______________________

Mixed Review!

_____ ÷ 9 = 4 9 x _____ = 108 _____ + 7 = 16

43 + _____ = 60 500 – 17 = _____ 27 – _____ = 18



Practice with factoring!Fill in this chart. The first one is done for you.

Number Pairs of Factors Factors

6 1 x 6 2 x 3 1, 2, 3, 6

12

18

25

27

49

64

72

84

96

66

50

100

42

48

1 1



Review Time!

☐ Take the time now to narrate to your teacher everything you have learned about factoring.

Bonus Concept!In Lesson 7, we discussed converting measurements. When we are going from larger units of measure to smaller units of measure, we multiply, as seen in the example:

3 yards = 9 feetSince we know that 3 feet = 1 yard, we can multiply 3 x 3. So think: 3 groups of 3 yards.

Now you try it!

There are 5,280 feet in 1 mile. There are 12 items in 1 dozen._____________ feet = 2 miles _____________ items = 3 dozen

There are 60 minutes in 1 hour. There are 1,760 yards in 1 mile._____________ minutes = 24 hours _____________ yards = 8 miles

There are 12 items in 1 dozen. There are 60 seconds in a minute.36 items = _____________ dozen 3,600 seconds = _________ minutes

There are 2,000 pounds in 1 ton There are 12 months in 1 year10,000 pounds = ___________ tons 132 months = _____________ years

1 foot 1 foot 1 foot 1 foot 1 foot 1 foot 1 foot 1 foot 1 foot

1 yard 1 yard 1 yard


LessonSubtracting Mixed Numbers with Uncommon Denominators

24“But I don’t want them to go!” Ella’s voice trembled with sadness. “I’ll miss Danielle too much.”

“I know, Honey. Goodbyes are so very hard. But we will see them again! Soon! I promise. Come out from under the bed. You need to say goodbye to your Auntie and Uncle and cousins. Come on, Honey. Out you come. Good girl. Come here, let me give you a hug,” Maddie knelt in front of her small daughter and hugged her tightly. Goodbyes are so hard, she thought to herself. Nasty things.

“Goodbye, Uncle Justin. Goodbye, Aunt Kate!” Natty hugged first one and then the other. “I’ll miss you!”

“We’ll miss you, too, Natty. We’ll miss all of you!” Kate said through her sniffling. She hugged each of her nephews and nieces and then started around again.

“Kate! We have to go, Honey! We have to be at the airport in an hour,” Uncle Justin put his arm around his wife to try to steer her out the door. Ugh. Goodbyes are so hard, he thought to himself.

Maddie and all of the Stevens children stood at the door and waved goodbye to their family members. Sean Stevens was taking them to the airport.

The house seemed strangely quiet. Everyone was so sad!“Come on guys. Let’s try to cheer up! Should we play a game or something? What do you guys

want to do? Games? Puzzles? Anything?” When no one answered Mom, she decided to take things into her own hands. “Ok, well, let’s play this new game we got from Grandma and Grandpa for Christmas. It’s a banking game! Look, it even has little checkbooks for each of the players. Doesn’t this look fun?” she asked.

“Ok, I’ll play,” Charlie said sadly. “It won’t be as much fun without Sean and Abby, but that’s ok. We have to get use to them not being here...”

“Ok, I’ll play, too,” Charlotte sighed and sat next to Charlie. One by one the children pulled out chairs and sat down around the table.

“Let me start by reading the directions,” Mom said and tried to smile brightly at her children. Even Ella had pulled up a chair. After looking at the box lid to see how old she had to be to play, she went to get her new coloring book and crayons.

“Ella is so smart, isn’t she, Mom?” Natty asked, smiling at her little sister. “She knows how to check the age on a game. She saw that it says “8+”!”

“She is smart!” Mom agreed and smiled at Ella. The little girl’s eyes were still red from crying, but she smiled back and opened her coloring book to work on the picture she had started the night before.


“Here you go, kids; these are the little checkbooks we use to play the game,” Mom slid the checkbooks and pencils across the table to each of the older kids. “This is a really cool game! Look at this list of skills covered in the game! It says, ‘Writing checks, balancing bank accounts, addition/subtraction of decimals, and even work with fractions and whole numbers with uncommon denominators!”

“Hey, that’s what I was just teaching the girls the other day,” Charlie said. “I’m going to like this game! I can already tell! And, what do you know! Math was the answer to our problems again!” When everyone looked at him questioningly, he continued, “This game of math helped cheer us up! Math saves the day again!” Everyone was giggling by now. Charlie and his math! What a silly boy!

Later that evening, the family was gathered in the family room for their bedtime devotion time. Dad looked at Mom with a questioning look, and she nodded her head at him. The children looked from one parent to the other. Something was up!

“Kids, Mom and I have a surprise for you!” Dad said, leaning forward with excitement. “We are going to go on a three week adventure! We are going to go to a wilderness camp! Mom and I have been asked to come run a children’s survival awareness camp for children six to twelve years old. We have decided to go, and you all are coming with us!”

Whoops of excitement went up around the circle. Only Ella sat quietly.“Daddy, I’m not old enough to go,” Ella said with a quivering lower lip. “I’m not old enough to do

anything the other kids can. It’s like the game we got for Christmas! I’m too little to do anything.” Ella’s head hung down, and a single tear slipped off of the end of her nose.

“Oh Honey! You most certainly ARE going with us!” Dad picked Ella up and placed her on his knee. “Look at me, Ella. You are part of this family, and you are going! In fact, I told the camp owners that all of my children were coming, or none of us were coming. That’s what Mom and I decided. And that is what has happened. We are all going, Ella. Including you!”

Ella smiled through her tears and snuggled against her daddy’s chest. She didn’t mind being small after all. She was the only one of the children who could still snuggle up under her daddy’s chin. And that was a good thing!



New Concept!We cannot subtract 2 4

5 from 6 15 . Therefore, just like any other subtraction problem, we need to borrow. In

this problem, we borrow from the 6. The 6 becomes 5 55 . The five-fifths we borrowed from the 6 is added to

the 15 , making our new mixed number 5 6

5 . Now we can subtract.

Copywork.

We cannot subtract a mixed number problem when the top fraction is smaller than the bottom. Therefore, just like any other subtraction problem, we need to borrow. We borrow from the whole number, taking one “unit” from it and making it an equivalent fraction (with the bottom fraction). We then subtract, using the new mixed number as the minuend (top number).

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

____________________________________________________________________________________

615

– 2 45

565

– 245

325

55

#3 Move your whole

number over.

#4 Move this over, also. #5

Subtract

#1#25 5

5

+ =



You try it now!The first one is done for you. Reduce if necessary.

413

– 123

343

123

223

535

– 245

1 116

– 956

Mixed Review! Reduce and change improper fractions into mixed numbers.

49

23

+ 5

18

39

59

+ 1

18

1 1,050

– 2, 1 32

57,459

– 29, 09 1

Solve.

1,760 yards = _______ mile(s) 1 mile = _______ feet

3 miles = _______ yards 3 mile = _______ feet

108 items = _______ dozen 96 months = _______ years



More practice with the concept! Reduce if necessary. Narrate to your teacher what you are doing.

638

– 258

537

– 457

8614

– 5934

1019

– 389

Mixed Review!Turn these improper fractions into mixed or whole numbers.

427

638

254

173

3311

754

Reduce. Use your Reduce the Fraction! Chart if you need help.

427

638

254

173

3311

754

Add. Subtract.

783

236

+ 5 10

42 1

1 48

+ 664

3, 78 1– 2,989

78– 69



Adding onto the concept.

Study the problem above and try these. The first one is done for you. Reduce if necessary.

612 = 6

24 = 5

64

– 434 = 4

34 = 4

34

134

934

– 578

43

16

– 258

513

– 349

Mixed Review! Write as decimals. The first one is done for you.

51 100 = .51 23

100 = ______

1 100 =

______

Copywork for review!

In decimal place value, the place to the right of the decimal is the tenths place.

_____________________________________________________________________________________

_____________________________________________________________________________________

The second place to the right of a decimal is the hundredths place.

_____________________________________________________________________________________

_____________________________________________________________________________________Work with your Fraction, Decimal, and Percent Chart. Show these fractions as decimals and percents on your chart.

☐ 4 100

☐ 78 100

☐ 92 100

☐ 28 100

☐ 16 100

826

5 56

813

– 5 56

786

556

336

We have a mixed number problem with uncommon denominators.

#1 Find a common denominator.

#4 Reduce if necessary.

#3 Subtract.

#2 Since the top fraction is smaller than the bottom, we need to borrow from the whole number to make a bigger fraction.

7 66

===

=

=

312


Let’s Review! Reduce if necessary. Narrate to your teacher each step.

615

– 145

927

– 167

934

– 578

39116

– 18723

1698

15

– 5645

Write the following on a new index card and illustrate it.We cannot subtract a mixed number problem when the top fraction is smaller than the bottom. Therefore, just like any other subtraction problem, we need to borrow. We borrow from the whole number, taking one “unit” from it and making it an equivalent fraction(with the bottom fraction). We then subtract, using the new mixed number as the minuend (top number).Write these numbers in words.

301,568 _____________________________________________________________________________________

34,560_____________________________________________________________________________________

2,001_____________________________________________________________________________________

$46.56_____________________________________________________________________________________

$782.10_____________________________________________________________________________________




Sudoku!Take your time — and see if it is getting easier to do these puzzles! The next time you are at the library or a store, look and see what kinds of Sudoku puzzles are available. If you want to know more, you can research the history of the puzzles!

Teac

her

Have your student(s) work with any concepts he or she is having trouble with.

LessonReview of Multiplying and Dividing Decimals

36• Multiply as usual. Next, starting at the right, count the total number of decimal places in

both factors and count off that many decimal places in the product.• When we multiply decimals, we sometimes need to add a zero to the product to make enough

decimal places. Count from the right the number of decimal places needed, but there were not enough places. This is where we added the zero to the left side of the product.

• When we multiply money (with decimals), we use the same rules. When we find our product, however, we need to round to the hundredths place.

• When we divide decimals, we have to completely remove the decimal from the divisor.• In decimal place value, the place to the right of the decimal is the tenths place.




Review Time! Copywork:

Multiplying decimals...We multiply as usual. Next, starting at the right, count the total number of decimal places in both factors and count off that many decimal places in the product.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

Solve.

.9

x .4

7.25

x .3

3.42

x . 88

.642

x . 1 1

Write, in your own words, what you have learned about multiplying decimals.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________



.23

x . 1 5

.3 1

x . 17

.43

x . 1 6

.25

x . 2 1

.5

x .3

.12

x .6

17. 1

x 6

14.2

x . 8

Write what you have learned about adding zero to the product when multiplying decimals.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

We need to add a zero to make enough decimal places.

.1 2x .1 3

36 + 1 20.0 1 56

(2)

(2)

(4)

When we multiply decimals, we sometimes need to add a zero

to the product to make enough decimal places. Like this.

As you can see, we counted from the right the number of

decimal places needed, but there were not enough places.

This is where we added the zero to the left side of the product.

Review Time!



When we multiply money (with decimals), we use the same rules. When we find our product, however, we need to round to the hundredths place.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

$ 3.85

x .43

$ 7. 13

x . 18

$ 2. 1 1

x . 80

$ 2. 38

x . 27

Write what you have learned about multiplying money.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________





When we divide decimals, we have to completely remove the decimal from the divisor.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

The third place to the right of the decimal is the thousandths place.

_____________________________________________________________________________________

_____________________________________________________________________________________

Divide and check.

9 1 8 9. .

4 1 3 6. .

5 2 0 5. .



The Double Sudoku Challenge! Here is a variation on the simple Sudoku puzzles you have been completing. This is a Double Sudoku – which just means there are two Sudoku puzzles in one overlapped puzzle. We have outlined one puzzle in blue, and the other in green.

When solving this kind of Sudoku, the same rules that you have learned still apply. You just have to take into account both puzzles when finding the solutions for each. The most challenge portion of the puzzle will be the four 3 x 3 squares in the overlapped area (it is the shaded portion). Hint – use the numbers outside of the overlapped area as clues to find the missing numbers for each Sudoku!

When solved, both puzzles will be complete with no repeated numbers in the rows, columns, or 3 x 3 squares within the 9 x 9 green and blue puzzles. As always, if you are not sure about what to do, talk to your teacher and ask for help.

295Math Level 5 – Solutions Manual

Solutions Manual: Lesson 1



Mental Math

20 + 8 + 6 + 1 1 + 3 + 5 = 53 1 10 + 120 + 350 = 580

1,090 + 10 + 100 = 1,200 650 + 40 + 8 + 2 = 700

200 + 60 + 9 + 10 = 279 4,001 + 9 + 80 = 4,090

Facts review. Work quickly.

+ 4 6 10 8 2 3 5 1 9 7 0

6 10 12 16 14 8 9 1 1 7 15 13 6

+ 6 4 8 0 1 2 9 3 5 7 10

9 15 13 17 9 10 1 1 18 12 14 16 19

+ 2 5 8 1 10 3 6 4 0 7 9

8 10 13 16 9 18 1 1 14 12 8 15 17

+ 8 2 9 6 0 7 1 4 3 10 5

7 15 9 16 13 7 14 8 1 1 10 17 12



Addition review.

520

294+ 24

838

6 1 3

356+ 7 1 3

1,682

95,01 1+ 15,219

1 10,230

90,345+ 43,82 1

134, 166

38

25

35+ 14

1 12

24

3 1

26+ 1 5

96

4 1

86

26+ 38

191

Fill in the blanks. Write the subtraction equation you used to solve the problem underneath it. The first one is done for you.

8 + 7 = 15 5 + 6 = 1 1 4 + 10 = 14

15 – 8 = 7 1 1 – 5 = 6 14 – 4 = 10

9 + 8 = 17 7 + 5 = 12 9 + 3 = 12

17 – 9 = 8 12 – 7 = 5 12 – 9 = 3

10 + 10 = 20 8 + 8 = 16 8 + 9 = 17

20 – 10 = 10 16 – 8 = 8 17 – 8 = 9

3 + 8 = 1 1 2 + 10 = 12 7 + 9 = 16

1 1 – 3 = 8 12 – 2 = 10 16 – 7 = 9

1

2 2

1

1

1 11



Subtraction review.

9,000– 6,826

2, 1 74

3,055– 2,245

8 10

20,020– 1 2, 1 72

7,848

52,03 1– 1 0,729

4 1 ,302

Need more practice?

300– 144

1 56

600– 1 49

45 1

300– 226

74

Fill in the blanks. Write the addition equation you used to solve the problem underneath it. The first one is done for you.

17 – 8 = 9 12 – 6 = 6 16 – 9 = 7

8 + 9 = 17 6 + 6 = 12 7 + 9 = 16

16 – 8 = 8 20 – 10 = 10 15 – 6 = 9

8 + 8 = 16 10 + 10 = 20 9 + 6 = 15

14 – 5 = 9 13 – 5 = 8 5 – 0 = 5

9 + 5 = 14 8 + 5 = 13 5 + 0 = 5

21 – 10 = 1 1 19 – 8 = 1 1 18 – 3 = 15

1 1 + 10 = 21 1 1 + 8 = 19 15 + 3 = 18

1118 9 9 9 9 11

1

1 111 11

1 11 111112

2 259 99

2



Word Problems:1. When Grandpa Stevens took the children to the State Fair, they counted 24 big rides in one area of the

midway, 19 smaller rides in the children’s area, and 15 rides along the old-fashioned board walks in the “Ole’ Western Days” area. How many rides did they count all together at the fair?

2. How many more rides did they count in the midway than the children’s area?

3. At the fair, Charlie bought cotton candy for $1.75, Hairo bought an ice-cream cone for $2.25, and Charlotte and Natty combined their money to buy a funnel cake for $5.90. How much money did they all spend together?

4. How much more did the girls pay for the funnel cake than Charlie paid for his cotton candy?

5. What addition clue words do you look for in a word problem?

6. What subtraction clue words do you look for in a word problem?

24 + 19 + 15 = 58 rides all together

24 – 19 = 5 more rides

"How many rides did they count all together?""How much did they spend all together?"

"How many more rides…""How much more did…"

$1 .752.25

+ 5.90$9.90 all together

$5.90– 1 .75$4. 1 5

18

11

308 Math Level 5 – Solutions Manual




New Concept!Factors are all of the different numbers that divide evenly (without a remainder) into a number. Pairs of factors are two numbers that, when multiplied together, equal this number. Are you confused? Study these examples.Example #1: Find the factors of 15.

Pairs of Factors Factors1 x 15 3 x 55 x 315 x 1

1, 3, 5, 15

Example #2: Find the factors of 9.

Pairs of Factors Factors1 x 9 3 x 39 x 1

1, 3, 9

Now you try it!Find the pairs of factors of each of these numbers and list them in order from least to greatest.


1 x 8 2 x 4 4 x 2 8 x 1

1, 2, 4, 8

Pairs of Factors for 10 Factors 1 x 10 2 x 5 5 x 2 10 x 1

1, 2, 5, 10

When we list the factors, we write each one only once, from least to greatest.



1 x 7 7 x 1

1, 7

Pairs of Factors for 12 Factors 1 x 12 2 x 6 3 x 4 4 x 3 6 x 2 12 x 1

1, 2, 3, 4, 6, 12

Review!On Monday, Charlotte and Natty worked at their lemonade stand from 2:30 to 3:45 p.m. Then they worked at the library from 4:00 to 5:30 p.m. How long did they work on Monday?


1 hr. & 15 min.

all together

1 hr. & 30 min.

1 hr. 30 min.+ 1 hr. 15 min.

2 hr. 45 min.


Practice the new concept!Complete the pairs of factors for these numbers.

18 20 351 x 182 x 9 3 x 6 6 x 3 9 x 2 18 x 1

1 x 202 x 10 4 x 5 5 x 4 10 x 2 20 x 1

1 x 355 x 7 7 x 5 35 x 1

Now list the factors for each of the numbers above.

18 18, 9, 6, 3, 2, 1

20 20, 10, 5, 4, 2, 1

35 35, 7, 5, 1

Mixed Review!

Divide and write the remainders as fractions.

4 02 1 8 4 0

8 40 0

2 01 5 3 1 3

3 01 3

–

1315

Solve these mixed number problems.

203 1719

– 1 87 919

1 6 819

8738

+ 1 928

106 58


–

111 19



Copywork of new concept!

Factors are all of the different numbers that divide evenly (without a remainder) into a number. Pairs of factors are two numbers that, when multiplied together, equal this number.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

More practice of the new concept!Write the pairs of factors. Note: These numbers are called prime numbers. Their only factors are 1 and themselves.

5 3 7 1 1

1 x 5 5 x 1

1 x 3 3 x 1

1 x 7 7 x 1

1 1 x 7 7 x 1 1

Write any three factors for each of these numbers. Optional: write all of the factors for each of the following numbers.

24 1, 2, 3, 4, 6, 8, 12, 24 27 1, 3, 9, 2732 1, 2, 4, 8, 16, 32 64 1, 2, 4, 8, 16, 32, 64

Mixed Review!

36 ÷ 9 = 4 9 x 12 = 108 9 + 7 = 164 x 9 = 36 108 ÷ 12 = 9 16 – 7 = 9

43 + 17 = 60 500 – 17 = 483 27 – 9 = 1860 – 43 = 17 483 + 17 = 500 27 – 18 = 9

Copywork


Solutions Manual: Lesson 12 — Lesson 13



Practice with factoring!Fill in this chart. The first one is done for you.

Number Pairs of Factors Factors

6 1 x 6 2 x 3 1, 2, 3, 6

12 1 x 12 2 x 6 3 x 4 12 x 1 6 x 2 4 x 3 1, 2, 3, 4, 6, 12

18 1 x 18 2 x 9 3 x 6 18 x 1 9 x 2 6 x 3 1, 2, 3, 6, 9, 18

25 25 x 1 5 x 5 1 x 25 5 x 5 1, 3, 25

27 27 x 1 9 x 3 1 x 27 3 x 9 1, 3, 9, 27

49 49 x 1 7 x 7 1 x 49 7 x 7 1, 7, 49

64 64 x 1 2 x 32 4 x 16 8 x 8 1 x 64 32 x 2 16 x 4 8 x 8 1, 2, 4, 8, 16, 32, 64

72 72 x 1 2 x 36 3 x 24 4 x 18 6 x 12 8 x 9 1 x 72 36 x 2 24 x 3 18 x 4 12 x 6 9 x 8

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

84 84 x 1 42 x 2 28 x 3 21 x 4 14 x 6 12 x 7 1 x 84 2 x 42 3 x 28 4 x 21 6 x 14 7 x 12

1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84

96 96 x 1 48 x 2 32 x 3 24 x 4 16 x 6 12 x 8 1 x 96 2 x 48 3 x 32 4 x 24 6 x 16 8 x 12

1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96

66 66 x 1 2 x 33 3 x 22 6 x 11 1 x 66 33 x 2 22 x 3 11 x 6 1, 2, 3, 6, 11, 22, 33, 66

50 50 x 1 2 x 25 5 x 10 1 x 50 25 x 2 10 x 5 1, 2, 5, 10, 25, 50

100 100 x 1 2 x 50 4 x 25 5 x 20 10 x 10 1 x 100 50 x 2 25 x 4 20 x 5 10 x 10

1, 2, 4, 5, 10, 20, 25, 50, 100

42 42 x 1 2 x 21 3 x 14 6 x 7 1 x 42 21 x 2 14 x 3 7 x 6 1, 2, 3, 6, 7, 14, 21, 42

48 48 x 1 24 x 2 3 x 16 4 x 12 6 x 8 1 x 48 2 x 24 16 x 3 12 x 4 8 x 6

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

1 1 1 1 x 1 1 1 x 1 1, 1 1



Review Time!

☐ Take the time now to narrate to your teacher everything you have learned about factoring.

Bonus Concept!In Lesson 7, we discussed converting measurements. When we are going from larger units of measure to smaller units of measure, we multiply, as seen in the example:

3 yards = 9 feetSince we know that 3 feet = 1 yard, we can multiply 3 x 3. So think: 3 groups of 3 yards.

Now you try it!

There are 5,280 feet in 1 mile. There are 12 items in 1 dozen.5,280 x 2 12 x 310,560 feet = 2 miles 36 items = 3 dozen

There are 60 minutes in 1 hour. There are 1,760 yards in 1 mile.60 x 24 1,760 x 81,440 minutes = 24 hours 14,080 yards = 8 miles

There are 12 items in 1 dozen. There are 60 seconds in a minute.36 ÷ 13 3,600 ÷ 6036 items = 3 dozen 3,600 seconds = 60 minutes

There are 2,000 pounds in 1 ton There are 12 months in 1 year10,000 ÷ 2,000 132 ÷ 1210,000 pounds = 5 tons 132 months = 1 1 years

1 foot 1 foot 1 foot 1 foot 1 foot 1 foot 1 foot 1 foot 1 foot

1 yard 1 yard 1 yard



Building on the concept of factoring!A common factor is a factor that two or more numbers share. Complete the chart below. Circle the com-mon factors in each pair of numbers. Study the example below before you begin.

Number Pairs of Factors Factors Common Factors

61 x 6 2 x 36 x 1 3 x 2

1, 2, 3, 6The common factors

of 6 and 12 are:1, 2, 3, 612

1 x 12 2 x 63 x 4 12 x 16 x 2 4 x 3

1, 2, 3, 4, 6, 12

Now you try!


81 x 8 4 x 28 x 1 2 x 4

1, 2, 4, 8

1, 2, 4, 8

161 x 16 2 x 8 4 x 416 x 1 8 x 2 4 x 4

1, 2, 4, 8, 16


151 x 15 5 x 315 x 1 3 x 5

1, 3, 5, 15

1, 5

2020 x 1 2 x 10 4 x 51 x 20 10 x 2 5 x 4

1, 2, 4, 5, 10, 20



Divisibility RulesIn finding factors, divisibility rules are extremely useful! Therefore, in this week’s exercises, we will be making flashcards for each of the divisibility rules. These will help you to know which factors are in larger numbers. Today’s rule is about numbers that can be divided by 2, thus making 2 a factor.

Whenever you see this writing, you will be adding to your “Divisibility Rules” flashcards.

Thinking TOOLS!

Flashcard Copywork!

Can it be divided by 2?A number is divisible by 2 if it is an even number.

(Remember! Even numbers end in 0, 2, 4, 6, or 8.)

PracticeCircle the numbers that are divisible by 2. Use the rule you copied.

29 42

179 360

1,420 1,893

26,732,546 3,333,338





Work and narrate!

71924

+ 838

154

1924

924

2824

91112

+ 816

174

1112

212

1312

11021

+ 757

84

1021

1521

2521

☐ Thinking TOOL Card: Copy this concept onto a new index card.

Sometimes when we add two or more mixed numbers, the fractional part of the sum is an improper fraction. To find the final answer, we must “set aside” the whole number part while we turn the improper fraction into a mixed number. Finally, we add the two whole parts and place our fractional part next to it.

Review.Add. Subtract.

78

85

+ 92

255

10,565

+ 20,678

31 ,243

1,000,207

– 8 7 2, 1 98

1 28,009

Divide and check.

3 0 0 0 1 62 0 6 0 0 0 3 2 0

6 00 0 0 3 2

2 01 2 01 2 0

0

, ,,

–

–

–

= 16 424= 16

16 = 18

112 = 9

421

300,016

x 20

6,000,320

Fill in the blanks.

5 x 100 = 500

42 ÷ 6 = 7

480 ÷ 12 = 40

6 x 12 = 72

111

1

111 111 9999



You try it now!The first one is done for you. Reduce if necessary.

413

– 123

343

123

223

535

– 245

485

– 245

245

1 116

– 956

1076

– 956

126

Mixed Review! Reduce and change improper fractions into mixed numbers.

49

23

+ 5

18

818

1218

+ 5

18

2518

39

13

+ 1

18

618

618

+ 1

18

1318

1 1,050

– 2, 1 32

8,9 1 8

57,459

– 29, 09 1

28,368

Solve.

1,760 yards = 1 mile(s) 1 mile = 5,280 feet

3 miles = 5,280 yards 3 mile = 15,840 feet

108 items = 9 dozen 96 months = 8 years

= 113

= 17

18

1 11110 4 34



More practice with the concept! Reduce if necessary. Narrate to your teacher what you are doing.

638 = 5

118

– 258 = 2

58

368

537 = 4

107

– 457 = 4

57

57

8614 = 85

54

– 5934 = 59

34

2624

1019 = 9

109

– 389 = 3

89

629

Mixed Review!Turn these improper fractions into mixed or whole numbers.

427 = 6

638 = 7

78

254 = 6

14

173 = 5

23

3311 = 3

754 = 18

34

Reduce. Use your Reduce the Fraction! Chart if you need help.

48 =

12

927 =

13

1832 =

916

414 =

27

315 =

15

620 =

310

Add. Subtract.

783

236

+ 5 10

1,529

42 1

1 48

+ 664

1,233

3, 78 1– 2,989

792

78– 69

9

= 334 = 26

12

1 11 1 1

17

2 1617 6



Adding onto the concept.

Study the problem above and try these. The first one is done for you. Reduce if necessary.

612 = 6

24 = 5

64

– 434 = 4

34 = 4

34

134

934 = 9

68 = 8

148

– 578 = 5

78 = 5

78

378

513 = 5

39 = 4

129

– 349 = 3

49 = 3

49

189

Mixed Review! Write as decimals. The first one is done for you.

51 100 = .51 23

100 = .23 1 100 = .01

Copywork for review!

In decimal place value, the place to the right of the decimal is the tenths place.

_____________________________________________________________________________________

_____________________________________________________________________________________

Work with your Fraction, Decimal, and Percent Chart. Show these fractions as decimals and percents on your chart.

☐ 4 100

☐ 78 100

☐ 92 100

☐ 28 100

☐ 16 100

826

5 56

813

– 5 56

786

556

336

We have a mixed number problem with uncommon denominators.

#1 Find a common denominator.

#4 Reduce if necessary.

#3 Subtract.

#2 Since the top fraction is smaller than the bottom, we need to borrow from the whole number to make a bigger fraction.

7 66

===

=

=

312

.04 4% .78 78% .92 92% .28 28% .16 16%

Copywork




Let’s Review! Reduce if necessary. Narrate to your teacher each step.

615 = 5

65

– 145 = 1

45

425

927 = 8

97

– 167 = 1

67

737

934 = 9

68 = 8

148

– 578 = 5

78 = 5

78

378

39116 = 39 1

16 = 390

76

– 18723 = 187

46 = 187

46

20336

1698

15 = 1698

15 = 1682315

– 5645 = 56

1215 = 56

1215

1 1 21115

☐ Thinking TOOL Card Copywork (Write the following on a new index card and illustrate it.)We cannot subtract a mixed number problem when the top fraction is smaller than the bottom. Therefore, just like any other subtraction problem, we need to borrow. We borrow from the whole number, taking one “unit” from it and making it an equivalent fraction(with the bottom fraction). We then subtract, using the new mixed number as the minuend (top number).Write these numbers in words.

301,568 Three hundred thousand one, five hundred sixty-eight

34,560Thirty-four thousand, five hundred sixty

2,001Two thousand, one

$46.56Forty-six dollars and fifty-six cents

$782.10Seven hundred eighty-two dollars and ten cents


= 20312



Sudoku!Take your time — and see if it is getting easier to do these puzzles! The next time you are at the library or a store, look and see what kinds of Sudoku puzzles are available. If you want to know more, you can research the history of the puzzles!

Teac

her

Have your student(s) work with any concepts he or she is having trouble with.


Review Time! Review of all decimal concepts. Copywork

Fractions, decimals, and percents are three ways to name part of a whole. All three have numerators and denominators.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

1 dollar (whole) has 100 cents (parts).1 whole dollar is 100

100.1 whole dollar is 100%

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

Mixed Review:Divide and check. Add. Subtract.

6 0 06 0 3 6 0 0 0

3 6 00 0 0

$ ..$ $ 6. 13

3.56

+ 7. 1 3

$ 16.82

$ 52.03

– 1 0. 72

$ 4 1 .3 1


$ 6.00x 60

$ 360.00

1 1 1

Copywork

Copywork



Bonus Concept! Writing checks.Have you ever watched your parents or older sibling write a check? Well, here’s your chance to learn how to write one yourself!

Now you write one!

Review Time! Review of addition and subtraction.

625

294

+ 723

1,642

729

789

+ 1 24

1,642

6, 100

– 3,5 1 9

2,58 1

40,000

– 3,5 1 9

36,48 1

Write the name of the store or person you are writing the check to on this line.

Your signature goes here.

Your Name, Address, and Phone Number here

Your Name, Address, and Phone Number here

Date

The amount written in words

My Local Grocery Store

My Signature

65.12Sixty-five and 12/100 _______________________

1 11111 1112 3 995 10 991

(Make sure you use cursive and an ink pen when signing checks.)

Answers will vary.





Optional Math Crossword PuzzleSolve the math problems below to find the answers to the crossword puzzle.

ACROSS

1. 5,341 + 9,520 + 5,165 = _______________

2. 765 + 964 + 82 = _______________

3. 535 ÷ 5 = _______________

4. 620 x 4 = _______________

5. 215 + 365 + 624 = _______________

6. 42,262 + 52,799 = _______________

7. 2,678 + 7,322 = _______________

8. 9,428 x 4 = _______________

DOWN

1. 11,529 – 5,312 = _______________

2. 3,584 ÷ 7 = _______________

3. 4,374 x 5 = _______________

4. 10,001 x 8 = _______________

5. 90,000 – 68,913 = _______________

6. 81,000 ÷ 9 = _______________

7. 40,002 + 60,520 = _______________

8. 140 x 75 = _______________

2 0 0 2 6

2 5

2 1 8 1 1

1 0 7 2 4 8 0

8 0

7 0

1 2 0 4 9 5 0 6 1

1 1 0 8 0

1 0 0 0 0 0 0

8 5 0 5

7 0 2

0 3 7 7 1 2

1 1

2

2

3 4

3

4

6

8

8

7

7

5 5




Multiplying decimals...We multiply as usual. Next, starting at the right, count the total number of decimal places in both factors and count off that many decimal places in the product.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

Solve.

.9

x .4

.36

7.25

x .3

2. 175

3.42x . 88

2736+ 273603.0096

.642x . 1 1

642+ 6420.07062

Write, in your own words, what you have learned about multiplying decimals.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

Answers will vary.

1 1

1

1 1

3

Copywork



.23x . 1 5

1 15+ 230.0345

.3 1

x . 17217

+ 310.0527

.43

x . 1 6258

+ 430.0688

.25

x . 2 125

+ 500.0525

.5

x .3.15

.12

x .6.072

17. 1

x 6102.6

14.2

x . 81 1.36

Write what you have learned about adding zero to the product when multiplying decimals.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

We need to add a zero to make enough decimal places.

.1 2x .1 3

36 + 1 20.0 1 56

(2)

(2)

(4)

When we multiply decimals, we sometimes need to add a zero

to the product to make enough decimal places. Like this.

As you can see, we counted from the right the number of

decimal places needed, but there were not enough places.

This is where we added the zero to the left side of the product.

Answers will vary.

1 1

11 34

1

Review Time!



When we multiply money (with decimals), we use the same rules. When we find our product, however, we need to round to the hundredths place.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________

$ 3.85

x .431 1 55

+ 154001.6555

$ 7. 13

x . 185704

+ 7 1 301.2834

$ 2. 1 1

x . 801.6880

$ 2. 38

x . 271666

+ 4760.6426

Write what you have learned about multiplying money.

_____________________________________________________________________________________

_____________________________________________________________________________________

_____________________________________________________________________________________


= $1.66 = $1.28

= $1.69

= $.64

Answers will vary.

Copywork

1 1

11

15222

23






When we divide decimals, we have to completely remove the decimal from the divisor.

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_____________________________________________________________________________________

_____________________________________________________________________________________

The third place to the right of the decimal is the thousandths place.

_____________________________________________________________________________________

_____________________________________________________________________________________

Divide and check.

2 1 9 1 8 9

1 80 9

90

. ..

–

–

3 4 4 1 3 6

1 21 61 6

0

. ..

–

–

4 1 5 2 0 5

2 00 5

50

. ..

–

–

Copywork

Copywork

21

x .918.9

34

x .413.6

41

x .520.5

1



The Double Sudoku Challenge! Here is a variation on the simple Sudoku puzzles you have been completing. This is a Double Sudoku – which just means there are two Sudoku puzzles in one overlapped puzzle. We have outlined one puzzle in blue, and the other in green.

When solving this kind of Sudoku, the same rules that you have learned still apply. You just have to take into account both puzzles when finding the solutions for each. The most challenge portion of the puzzle will be the four 3 x 3 squares in the overlapped area (it is the shaded portion). Hint – use the numbers outside of the overlapped area as clues to find the missing numbers for each Sudoku!

When solved, both puzzles will be complete with no repeated numbers in the rows, columns, or 3 x 3 squares within the 9 x 9 green and blue puzzles. As always, if you are not sure about what to do, talk to your teacher and ask for help.

Documents

Math Lessons for a Living Education: Level 5